Uncertainty quantification for lee wave drag due to spectral parameterization of the abyssal hill topography

Stratified steady geostrophic flow generates oceanic lee waves when it impinges on small-scale seafloor topography called abyssal hills. Quantifying lee wave drag is important in global ocean modelling because it has been shown to significantly influence the near-bottom energy dissipation, turbulence structure and consequently the mixing of nutrients. A major source of uncertainty in lee wave drag prediction is the unknown abyssal hill topography due to the limited spatial coverage of high-resolution bathymetric measurements. Abyssal hills are represented in global circulation models by a spectral model, which involves uncertain parameter values. In this study, we quantify the parametric uncertainty of the spectral model in one-dimensional form using the Maximum A Posteriori method. This method not only gives the best estimates of the parameters, but also their distribution and confidence intervals. It is advantageous over the least square method used in previous studies, as it considers the parameters to be random variables and estimates their density and corresponding confidence intervals based on the available data. In addition, it does not rely on the empirical calculation of the spatial correlation of the bathymetry. The algorithm is validated by synthetic bathymetry data generated from the spectral model, and the high-resolution bathymetry data of the southeast Pacific is used as a test case for quantification of the parametric uncertainty of the abyssal hills. The resulting parameter distributions can then be propagated to lee wave drag in ocean models. This study is the first effort to quantify the uncertainty of lee wave drag, and the method can be readily extended from regional to global scale simulations.